Theory-enriched practical knowledge in mathematics teacher education Oonk, W.

teacher education

Oonk, W.

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Oonk, W. (2009, June 23). Theory-enriched practical knowledge in

mathematics teacher education. ICLON PhD Dissertation Series. Retrieved from https://hdl.handle.net/1887/13866

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3 The exploratory studies

3.1 Introduction

The two exploratory studies, the first two links in the chain of four studies in this thesis, were part of the national Multimedia Interactive Learning Environment (MILE) project for primary mathematics teacher education in the Netherlands (Dolk, Faes, Goffree, Hermsen & Oonk, 1996). Both studies are described below in the context of the development of the MILE-project, with a focus on the two exploratory studies in sections 3.5, 3.8 and 3.9.

When designing learning environments in primary teacher education, there is an attempt to represent real teaching practice in an authentic and natural way to prospective teachers (see sections 2.4 and 2.7). When constructing these environments, teacher educators have to consider how to best motivate the student teacher, identifying the most relevant practice-based principles and the ways in which the theory and practice can be bridged (see the sections 2.4 up to 2.7). There are other considerations as well. For example, in the Netherlands, as in some other countries, teacher education is changing drastically.

Controversial teacher education curricula, consisting of primary school subjects originated after more than one hundred years of reflection on the subject matter of primary education and the ways teachers have taught, have been replaced. The new curricula intend to improve the general professionalization of the prospective teacher, for the most part neglecting the school subjects (section 2.5). More specifically, the new objective is to adequately prepare students to become competent beginning teachers.

In this chapter, we will describe how a learning environment focused on representing various teaching practices to prospective teachers, known as the MILE project, was inspired, designed, implemented, tested, and refined. Exploratory studies were important in the support of these processes.

Before describing the making of MILE and presenting details about its pedagogy and technology (section 3.3), we first provide some theoretical background on the development of MILE in the context of the theory-practice discussion of primary mathematics teacher education, following what has been argued in section 2.4 and 2.5.

iThis chapter has been published in adapted form as: Oonk, W., Goffree, F., & Verloop, N.

(2004). For the enrichment of practical knowledge. Good practice and useful theory for future primary teachers. In J. Brophy (Ed.), Using video in teacher education. Advances in Research on teaching. Vol. 10 (pp. 131-168). New York: Elsevier Science.

MILE is rooted in the Standards for Primary Mathematics Teacher Education (Goffree

& Dolk, 1995). The process of developing these standards and subsequent discussions provided the contributing teacher educators with opportunities to articulate pedagogical ideas and expand their repertoire of theoretical orientations. Furthermore, these developments appeared to provide new inspiration (Barnett, 1998; Goffree & Oonk, 1999, 2001; Herrington et al., 1998; Lampert & Loewenberg Ball, 1998; Mousley &

Sullivan, 1996), so the process was generative.

One of the areas that dominated team discussions was the concept of practical knowledge (see section 2.3.4), used to indicate the network of knowledge and insights that underlie teachers’ actions in practice (Elbaz, 1983; Fenstermacher, 1994; Verloop, 1992). Within this concept of practical knowledge, the concept of educative power, used by Cooney (2001b) and Jaworski (2001), is particularly applicable. How to help prospective teachers acquire educative power is an important question for educators.

The factors that motivate teachers often remain hidden as tacit knowledge (Elbaz, 1991), even if researchers ask about them, although sometimes they are revealed in teachers’ talk about practice. Those who listen well to reflective practitioners describe their teaching (see for example Lampert, 2001) will get a sense of (situated) practical knowledge. Such practical knowledge can be considered as a “narrative way of knowing” (Gudmundsdottir, 1995, 1996; Carter, 1993). The designers of MILE (Dolk et al., 1996) adopted this idea, which would have consequences for the content and format of MILE and also for the use of the learning environment by the student teachers.

Given the assumptions that practice plays a central role in teacher education curriculum and that acquiring practical knowledge is the main learning goal, it follows that teacher training colleges should incorporate useful representations of real teaching practice.

What real teaching practice means has been described in many ways (Lampert &

Loewenberg Ball, 1998; Masingila & Doerr, 2002; Herrington et al, 1998; Barnett, 1998), but in general, it means that all aspects of mathematics education in school are present, including such things as the teacher’s preparation and reflections, students’

notes, and when possible, interviews with teachers and students regarding their experiences of the lessons.

Many publications are available about representations of practice, recently in relation to the use of cases in teacher education (Walen & Williams, 2000). Some authors emphasize showing ‘good’ practice in these cases (Goffree, Oliveira, Serrazina &

Szendrei, 1999). This appears to force one to choose between ‘authentic’ and ‘good,’ a dilemma that can be reconciled if authentic is considered as ‘full professional practice’

and good as ‘good for student teachers.’ Selecting practical situations evokes the concept of situated cognition about knowledge within the situation and the idea of situated learning about eliciting knowledge from practice (Brown et al., 1989; Borko &

Putnam, 1996; Herrington et al, 1998; Leinhardt, 1988; Tzur, 2001).

New technology creates possibilities for adding an extra dimension to narrative representations of practice. Beyond written cases are multimedia narratives, in which educational stories are told in sound and picture, sometimes connected with text. Student teachers have opportunities to reflect on this recorded practice and to write their own interpretations and analyses, eventually related to their own teaching practice (Pi-Jen Lin, 2002; Mason, 2002). How to make the learning environment of student teachers educative (Lampert & Loewenberg Ball, 1998) has been discussed recently (Cohen 1998; Sullivan, 2002; Masingila & Doerr, 2002; Pi-Jen Lin, 2002). One strategy for making the environment educative is to engage learners in investigations with the support of an on- line tutor or expert. Following this initial process, student teachers have the opportunity to constitute a community of prospective teachers in order to discuss their investigations of their own classroom practice, which will provide motivation to learn from it (Brophy, 1988). Teacher educators and researchers assume that this process leads to reflective practice (see section 2.2) as output (Beattie, 1997; Griffiths & Tann, 1992; Jaworski, 1998, 2001; Krainer, 2001; Schön, 1983). However, the process does not always produce the intended results. For example, stories of other teachers’ practice often do not stimulate meaningful discourse. Student teachers often believe that they can manage their professional work as a matter of common sense (Lampert & Loewenberg Ball, 1998), so they fail to appreciate the need to articulate a theory of practice.

Researchers (and educators) look for ways to put student teachers in touch with relevant theory outside of practice (see chapter 2). For example, Donald Schön (1983;

1987) suggested linking theory to practice during ‘reflective conversations’ with practical situations. Others have developed the concepts of ‘practical theorising’

(Alexander, 1984; Ruthven, 2001; see section 2.7.1) or ‘theoretically grounded reasoning’ (McAninch in Masingila & Doerr, 2002, p. 241). Lampert (1998b) speaks of ‘thinking practice’ (p. 53) that is ‘integrating reasoning and knowing with action’

(Loewenberg Ball, 2000, p. 246). Professionals cannot constrain themselves to telling stories about practice using only the language of practice (Verloop, 2001). Theory cannot be omitted (Cooney, 2001a). Teachers need flexible cognitive structures (theory) to understand the information they derive from their complex and uncertain teaching practice (Spiro et al., 1988).

The next question for the designers of MILE was which theoretical framework student teachers needed to help them adopt a professional approach to practice. By starting modestly and leaving higher levels of theory in action for later (Leinhardt et al., 1995;

Oonk, 1999), teacher educators can focus attention on a framework of theoretical concepts to use for deriving meanings from practice (see also section 2.6). Student teachers must be provided the opportunity to assimilate the theoretical framework into

their practical knowledge, so that practice and theory will be integrated naturally (Dewey, 1933; Daniel, 1996; Leinhardt et al., 1995; Selter, 2001; Thiessen, 2000).

Having discussed the roots of MILE in research on cognitive structure and the assimilation of a theoretical framework, we describe in the next sections our efforts to make MILE’99 educative on the basis of continuing development, including exploratory investigations. In the last section (3.9) we explain how theory completes thinking on practical knowledge in the context of a new learning environment and the perspective of new research.

3.2 Prior development and research

3.2.1 Developing good practice

We begin by providing some background on our view of good practice in mathematics education.

The contents of good practice were developed as a response to reaction to the problems with the world-wide New Math movement in the 1960s and inspired by Freudenthal’s ideas (1978) about a new approach to mathematics education, embodied in what is now called as Realistic Mathematics Education (RME) (Treffers & Goffree, 1985; Treffers, 1991; Streefland, 1993; Gravemeijer, 1994).

Three late twentieth-century developments provided the foundation for MILE:

- developmental research in the Wiskobas project;

- the formulation of national core objectives in the Netherlands;

- the discussions on a new publication about ‘a National Programme for Mathematics Education on Elementary Schools.’

Developmental research

In the Wiskobas project (1970-1980; note 4), a new mathematics curriculum for primary schools was developed with the support of Freudenthal. It resulted in a concrete realistic program that describes a clear image of good practice in five learning-teaching (L-T) principles (Treffers, 1991).

L.1 Construction. Learning mathematics is a constructive activity.

T.1 Concrete basis for orientation. Make mathematics concrete. Create recognizable contexts to which children can assign their own meanings.

L.2 Raising the level. Learning mathematics takes place somewhere between the informal mathematics of the children themselves (intuitive notions and self- invented procedures) and the formal mathematics of adults.

T.2 Models. To be able to achieve the required raising in level during the teaching- learning process, the pupils must have at their disposal the tools for bridging the gap between informal and formal mathematics (Gravemeijer, 1994).

L.3 Reflection. Learning mathematics is stimulated by reflection. Reflection is, as it were, the engine for raising the level (Freudenthal, 1991).

T.3 Reflective moments. The teacher finds the right times to bring reflective moments into mathematics teaching. Good occasions for reflection include any cognitive conflicts that might occur and anything the pupil may have thought of independently (‘own productions’) (Streefland, 1991; Selter, 1993).

L.4 The social context. Children learn more often than not in the company of adults or other children. This means that other actors in the learning environment can provide the impulse for learning. As the different actors communicate with each other about mathematical concepts and procedures, they argue about them and come to insights collectively.

T.4 Interactive mathematics lessons. The teacher organizes mathematics education such that interaction becomes a natural part of it. This, in turn, creates a pedagogical climate in which all the pupils can take part in the interaction. The concept of a classroom as a sort of ‘mathematical community’ gives it an extra dimension, as does the Mathematical Conference in the class described by Selter (1993).

L.5 Structuring. If children construct their own meaningful mathematics, then new knowledge and insights become incorporated in what they have already learned.

This means that the available mathematical knowledge (think, for example, of cognitive structures) is subject to constant upgrading. The new knowledge is fitted into the existing cognitive structure (assimilation) or the total structure is adjusted to accommodate the new insights (accommodation). Also, one aspect of learning is the task of bringing structure to what is being learned.

T.5 Interweaving the strands of learning. The teacher bases mathematics teaching on real-world situations, both as sources of ideas and as places to apply them. The first case would be an example of ‘horizontal mathematizing.’ Further, the mathematical ideas being used can themselves form the subject matter (vertical mathematizing). This brings connections with other mathematical ideas into the picture, partly as a result of the concrete background.

At the very end of the century (Goffree & Frowijn, 2000) ‘good practice’ had to be defined again, but this time with the intention to create an instrument for self-evaluation in schools. For this goal the principles were elaborated into more refined statements, called ‘indicators’ of realistic mathematics education, used to observe and analyze mathematics teaching in classrooms.

- The teacher is teaching mathematics by problem solving.

- Problems are introduced in familiar contexts.

- A substantial part of the effective learning time is used to explore the context.

- While exploring the context of a problem the non-mathematical aspects mentioned by students are also considered.

- The context gives meaning to the mathematical activities.

- Introduction, problem setting, problem solving, and subsequent discussion are realized in interaction with the whole class.

- In order to stimulate mathematical activities in cooperative groups, the teacher creates reasons for the students to discuss, to explain, to cooperate, to convince each other, and to distribute tasks properly.

- Sufficient learning time is spent on the introduction and exploration of ‘models’.

- The use of concrete models (e.g., schemas such as number line, reckon rack, or fraction strips) results in the use of mental models.

- The teacher continuously anticipates students’ reactions during interactive class discussion.

- The pedagogical climate allows children to make mistakes and the teacher to overtly discuss these errors and their possible causes.

- The teacher takes time for reflective moments during the mathematics class.

- Students are stimulated to create mathematical problems themselves (e.g., for peers) and also to solve these problems reflectively.

- Teacher and students have an open mind for other people’s solutions.

- Frequently asked questions are “Why?” and “Are you sure?”.

The provoking character of ‘cognitive conflicts’ is used to challenge children’s thinking.

The formulation of national core objectives

Increasing attention to quality management in primary education is the second development to consider. The National Institute for Curriculum Development in the Netherlands (SLO) published, after a national debate in the different domains, a list of core objectives for the school subjects (SLO, 1993; Treffers, De Moor & Feijs, 1989).

National Programme for Mathematics Education on Elementary Schools

A subsequent publication showed how to teach ‘in the spirit of Wiskobas’ in order to realize the core objectives: Standards for primary mathematics education (Treffers et al., 1989; Treffers & De Moor, 1990). These standards fueled a broad debate about

‘realistic mathematics education,’ that resulted in widely accepted and theoretically founded views of ‘good practice in realistic mathematics education.’

3.2.2 Good practice for teacher education

During the Wiskobas project, teacher educators participated in the research and development. Freudenthal supported these activities; he participated in field tests and increasingly viewed student teachers’ learning processes as an emerging outcome of

mathematizing and didactisizing (Freudenthal, 1991). Thus in the years of Wiskobas a new approach to primary mathematics teacher education was designed, in close connection to the creation of realistic mathematics education (Goffree, 1979).

Following the Standards for primary mathematics education and the Standards for mathematics evaluation and teaching (NCTM 1989, 1992), the Dutch Association of Primary Mathematics Educators (NVORWO) submitted a request to the National Institute of Curriculum Development (SLO) to draft a similar publication specifically for Dutch teacher education. In 1990, a group comprising ten mathematics educators started developing national standards and presented the results to colleagues as a handbook for teacher educators (Goffree & Dolk, 1995).

The philosophy of teacher education elaborated in the handbook is founded on three pillars: a teacher education adaptation of the socio-constructivist vision of knowledge acquisition, reflection as the main driving force of the professionalization of teachers (Schön, 1983, 1987) and the interpretation of practical knowledge as a way of narrative knowing (Gudmundsdottir, 1995). The statement “Real teaching practice has to be the starting point of teacher education” is emphasized. In the attempt to elaborate this principle into concrete curriculum materials for student teachers, an essential question still remained: How can curriculum designers give a learning environment a ‘natural’

aura? And next: what do we mean by ‘natural’? Student teachers’ fieldwork practice is natural by definition, but when they discuss this practice, they often stick to a superficial interchange of ideas and opinions (Verloop, 2001). Rarely do these discussions reach a level of theoretical reflections.

Learning in practice is mostly a solo task because student teachers not often have the opportunity to discuss common experiences and observations. Moreover, they usually focus on fulfilling responsibilities and on survival issues, so talk about actions dominates their reflections on the profession. As a result, they do not acquire practical knowledge that can be generalized across situations or organize their narratives of teaching into a broader framework.

The group of ten Dutch teacher educators got a new perspective on this problem when they visited the School of Education of the University of Michigan. They were introduced to the Student Learning Environment (SLE), created by Lampert &

Loewenberg Ball (1998), which became a source of inspiration for the making of MILE.

Using the records of real teaching practice the Michigan student teachers could access a whole year of mathematics teaching, with options to observe teaching and learning from different points of view (teacher, students, subject matter, curriculum, classroom climate, et cetera.).

Although MILE would become a quite different learning environment than SLE was in 1995 (Goffree & Oonk, 2001), MILE is based on a similar philosophy about the

presentation of real teaching practice in teacher education: “good practice for student teachers learning about teaching primary mathematics in the spirit of realistic mathematics education.” Knowing this, it was important to make video recordings of practice without losing quality.

3.3 The making of MILE

3.3.1 Introduction

We began with the intention to create a similar multimedia learning environment for Dutch teacher education. The funds for a quick start were provided by the Dutch Government, and a project team (four math teacher educators and two technicians) (Dolk et al., 1996) worked on the first stage of the MILE project over the next 18 months.

The 40 Dutch Colleges of (Primary) Teacher Education were informed and invited to participate²³. The majority expressed a desire to do so. In November, 1996 the first mathematics lessons were recorded and the MILE team again visited Michigan, this time to investigate the Student Learning Environment in action and to discuss the theoretical background, the making of, and specifically the use of the Student Learning Environment in the framework of ongoing methods courses at the university. Student teachers there perform ‘open’ investigations based on personally formulated problems to investigate and questions to answer. The tutor (a teacher educator or graduate student) supervises these open investigations, and regularly annotates (via comments in

‘Word’) the reflective reports that the student teachers submit. Student teachers’

learning is optimal during these electronic discussions about observations and interpretations (Lampert & Loewenberg Ball, 1998).

3.3.2 Preparing the recording of good practice

Before the first video could be recorded in the classroom, decisions had to be made about subject matter (what is relevant?), the teacher (who is representative?), the school (as typical as possible and within easy reach). We wanted the school, the teacher, and the textbooks and manuals in use to reflect the situations student teachers ordinarily meet in primary schools. Toward this end, we asked all mathematics teacher educators in the Netherlands to answer three questions: (1) Describe the most appropriate practice school for your student teachers learning to teach mathematics, (2) Sketch a profile of the ideal primary school teacher to be a mentor (tutor), and (3) Consider the best teaching-learning situations you like your student teachers to see, to experience, to investigate, and to practice.

Responses to these questions suggested that good practice for student teachers should present interactions between actors in the classroom, the teacher’s numeracy and mathematical attitude, his/her pedagogical and didactical expertise, and the teacher’s

and students’ attitudes towards mathematics. There also were many ideas about the supervision and coaching of student teachers during fieldwork. With the results of this questionnaire in mind, the team members visited elementary schools, talked with headmasters and teachers, and made additional observations in classrooms. In discussions after each math class, specific attention was paid to the degree to which the teachers were able to reflect on their actions and to put their thoughts into words.

An elementary school in Amsterdam, appeared to be a good location for the first five weeks of shooting video in grade 2. Some time after the choice had been made, a lucky incidental circumstance was recognised: two teachers in grade 2, sharing one job, created a ‘natural’ setting for observing reflective practice (Jaworski, 1998, 2001;

Krainer, 2001). In order to keep continuity in students’ learning processes, they discussed subject matter and the performances of children regularly.

Also, thanks to the headmaster’s efforts, the MILE project was adopted by all (41) teachers of the school and members of the MILE team were accepted by the parents (grade 2) as well. The wish to do something in return for the school and also the intention to create a positive working climate for filmers, educators, teachers, and students was realised by offering four workshops as part of an in-service course.

‘Enlarging your practical knowledge of realistic mathematics teaching’ was the workshops’ focus. The teachers mentioned four themes: explaining, contexts, models, and interaction in a math class. This focus on practical knowledge typified the MILE team’s discussion and study. Practical knowledge is tacit knowledge; it becomes visible only in the actions of the teacher and during rare moments when teachers are telling stories of what happens in and around their classrooms. In the latter cases, the practical knowledge is hidden (wrapped) in their personal narratives (stories). Our two grade 2 teachers, sharing one job, would be able to reveal much of the practical knowledge that had been inspired by their transfer meetings.

The parents (grade 2) got serious attention from MILE. One parents’ evening was recorded in its entirety and became an integral part of MILE. On that evening the parents watched an earlier recorded grade 2 lesson. Then both teachers presented themselves as reflective practitioners and explained what happened in the classroom, told about underlying objectives, and invited the audience to ask questions about their children, the teachers’ actions, and the subject matter.

The lessons to be recorded were prepared in general outline by teacher and project director, not to model the ideal teacher, but to increase teachers’ self esteem. It is comparable to the approach of Lampert and Loewenberg Ball (1998): they didn’t want to be the model of a teacher to imitate, but indeed they want to be good teachers with their own (personal) practical knowledge of which student teachers could learn from. So the idea was that good practice for teacher education is not good practice to imitate.

The teachers agreed to follow the textbook and manual, but also add a ‘problem of the week.’ Every Wednesday during the five weeks of recording, the teacher would present an ‘open’ problem in order to stimulate interaction, problem setting, and problem solving in whole-class discussions and in small cooperative groups.

3.3.3 The scenario

To prepare the real time recordings, a shooting script (scenario) was compiled describing sequences of students’ and teacher’s actions during a lesson. The parents gave permission to take videos of their children and a professional film institute with experience in school classes was engaged.

The script appeared to be a useful advance organizer for all concerned, although once the lessons began, it unfolded naturally and was taped without interruption or script consultation. Scripting the scenario offered another advantage: becoming aware of the different positions of the cameras, the use of zooming in and out, the need for a clear lesson structure, the visibility of learning aids in the classroom, and the planning of fixed time periods (linked to the video tape length).

Three professional filmers operated two mobile cameras, one fixed camera, and the audio apparatus. One mobile camera just followed the teacher; the other focused on individual students or small groups. The fixed camera continually recorded wide-angle shots of the whole classroom. Because children in grade 2 do not speak ‘loud and clear,’

small microphones were set on the tables, hidden in small pots with plants.

The MILE educators planned with the filmers about how to capture the essentials of math classes and accomplish the general goal of making records of good practice every day during the next five weeks. The filmers had to be prepared to capture interesting events such as: children handling manipulatives, the teacher using models on the blackboard, subtle moments of help, interactions between people in the classroom, rising levels, spontaneous expressions of pupils, et cetera. Special attention has been asked for the narrative aspect of registrating, that means ‘thinking in stories’ while taping, i.e.

anticipating the narrative that might be developed later to weave together the segments they were taping. Furthermore the ‘integrity of practice’ was a point of attention to the preparation of the lessons; the filmers’ stance towards teacher and children was discussed:

they should find a balance between commitment (to taping children and their learning processes) and distance (in order not to influence the events in the classroom). Keeping a distance proved difficult, because the camera operators became popular guests. In no time they learned the children’s names and personal characteristics.

The project team chose to compromise between ‘shooting a Hollywood movie’ and simply recording everyday classroom interaction, searching to achieve a balance between recording authentic practice and recording representations of practice that would be optimal for use in educating student teachers.

3.3.4 The screen-test

One day was spent finding out the most appropriate camera positions, the audio management, the director’s tasks, and rehearsing the recording of a math class. Teacher and students in the try-out lesson rapidly got used to the presence of three cameras, an audio installation and three filmers, but it is difficult to estimate how such circumstances influence the daily routine. Children sometimes showed awareness of being taped, even after weeks of daily recordings. Also, the teachers confessed to being more careful during their interactions with children, particularly when disciplinary measures had to be taken or when values and standards had to be discussed.

One day the teacher had to comment on the negative attitude of one of the students in a small peer group. Afterwards she explained: “I do not like approaching Sandra in front of the camera the way I do in ordinary circumstances. I do not want to hurt either Sandra or myself.” Her colleague agreed: “You and I act less naturally in situations like that. Usually I say, raising my voice, ‘Stop it now!’ In front of the camera I first count to ten before speaking.” And, referring to a recent experience celebrating Santa Claus in the classroom, she said: “I usually act the fool with the children, but this time I found myself rather reserved.” In his report, the director reflected on these confessions: “It appears that the recording violates the intimacy of the classroom atmosphere. Keeping the situation natural requires specific preparation and coaching of the teachers involved.” (Oonk, 1997).

The rehearsal was very helpful in organizing the communication between the director outside and the filmers inside the classroom. Three purviews on classroom teaching had to be considered: the teacher’s point of view, looking over a student’s shoulder, or watching as an outside researcher does. Because our focus was on researching good practice for future teachers, the teacher’s viewpoint was considered to be the most relevant. In zooming in and out of the scenes, we used overall shots, half-total shots, and close ups. The half-totals usually were the most informative, such as a half-total shot of a small group at work or the teacher questioning one or two students. Close ups clearly show non-verbal expressions or the details of students’ seatwork. Overall shots were used afterwards, when editing the tapes to show transitions between activities or when inappropriate half-totals or close ups had to be replaced.

3.3.5 Recording and editing

Creating a representation of real teaching practice, such as the Student Learning Environment in Michigan required recording more than the math classes themselves:

the teacher before beginning the lesson telling what has been prepared; the ‘transfer’

discussions between the two job-sharing teachers; individual students practising basic facts in the workstation with a computer; interviews with students immediately after finishing a class, reflecting upon the lesson; a parent talking with the teacher about a

child; a teacher discussing a low achiever with the remedial teacher; a team discussion about interaction as a means to discuss good practice of realistic mathematics education;

celebrating Santa Claus at school, et cetera.

Sitting in a corner in the corridor, specially equipped with headphones, a microphone, and three monitors, the project director coached the filmers in the classroom. As a didactic expert, former teacher, and teacher educator, this director/researcher was focused on capturing the children’s learning processes, with an eye toward using the video with future student teachers. In contrast, the filmers were concerned mostly about the quality of the pictures.

After directing the recording of the math class and the attached activities to complete real time teaching, the director wrote notations into a reflective report, describing the events and adding ideas about how the tape might be used with student teachers. In other words, he already was thinking about making MILE educative, drawing inspiration from reflecting on recently directed recording. His report also was helpful for the editorial work. Three videotapes, recording the same events but from different points of view, had to be merged into one record of (good) practice; to maintain three different ‘streams’ as an alternative for the student teachers’ learning environment was too complicated as a representation of real practice. The report provided guidance for making the right choices and not missing any essentials. The director’s report kept focus on the narrative character of the practical knowledge perspective. A classroom plan and photographs of the pupils were necessary to keep orientation while editing. The reflections on recording and editing recorded in the director’s report were published (Oonk, 1997)²⁴.

3.3.6 Making the records of real teaching practice accessible

After editing, the videotapes had to be digitized so that the benefits of IT-technology could be used. Then an essential problem had to be dealt with: how to make this voluminous and still growing video material transparent and accessible for students in teacher education (Hermsen, Goffree & Stolting, 1997). IT-technology solved the problem by offering a search function capable of full text retrieval. Also, much time had to be spent writing texts close to the existing visual material, and IT-technology once again was of great help. The technicians in the team designed software to divide the videos into short sections (video fragments). The events in these sections could be described (in what formerly were called

‘titles’) as mini-stories, making use of keywords that could guide student teachers to these sections later. The desired length of the video fragments and linked mini-stories was considered in the context of facilitating the development of practical knowledge. The minimal size of a section was called ‘a narrative unit’ and the rule of thumb became

‘complete meaningful mini-story (narrative) with size between one and three minutes,’ as small as possible to create the possibility for a subtle search, but not so small that the

fragments would lose their meaning. Experience using the search engine indicated that students typically began with one mini-story and then wanted to view video fragments that came immediately before or after the mini-story just viewed. Consequently, the system was improved to make it easier for students to shift from the segment just played to adjacent segments of the same lesson.

An example: In one mini-story, grade 2 student Chantal is called on to draw the position of the number 45 between 40 and 50 on the number line. The mini-story says: “Chantal is measuring to find the position of 45 on the number line. She first estimates the middle between 40 and 50 to be sure. Minke gives praise and asks the other students to look carefully to the jump of ten.”

Student teachers, making their investigations in MILE, can watch the previous and next within a sequence of mini-stories that together represent a substantive part of the math class. It is also possible to combine stories from different places to create whole cases.

Thus the search function can be used in two different ways. The first brings the MILE investigator to the archive, in which dated lessons divided into sections (and other data) are organized chronologically. One can browse through the mini-stories and, if one seems interesting, click to the linked video fragment. It is also possible to find a fragment by typing a keyword (all mini-stories containing this word are shown). Each mini-story in this list is linked with the archive again, so it is possible to see the whole lesson in which it was embedded.

Making the records of real teaching searchable in this way converts ‘good practice’ into

‘good practice for use in teacher education.’ It also connects ‘good practice’ to

‘practical knowledge’ as a way of narrative knowing (Gudmundsdottir, 1995). In the next section, MILE is discussed in terms of good practice, as a starting point for exploring and thinking about making MILE educative.

3.4 MILE, a digitalized teaching practice

The heart of MILE can be considered as a digitalized ‘representation of full practice’

that provides examples of ‘good practice’ for use in teacher education. Looking back on the process of development we notice some characteristics of good practice.

Showing authenticity with real practice in schools. MILE deals with daily life in classrooms with ‘ordinary’ teachers, teaching in a realistic mathematics education vein, confronted with problems and dilemmas (Lampert, 1985), and with pupils both doing good things and making mistakes. It shows authentic practice, comparable with the practice that student teachers will experience.

Representing the complexity of real teaching practice. The ‘full practice’ represented in MILE reflects the complex reality of teaching (Lampert, 2001; Uhlenbeck, 2002).

Nearly all of the components that Lampert mentioned in her extended model of the didactic triangle (2001, chapter 14) are included, and there was an attempt to represent all areas of subject matter as well. The same attention to completeness applies to general pedagogic issues and the mathematical learning processes of pupils. Teachers reflect on their practice and pupils react during classroom discussions and in small group work.

Textbooks and teachers’ guides are available and in relevant situations one can meet other teachers of the school team, the headmaster, the counselor, or parents.

In the vein of realistic mathematics education. The five previously mentioned learning- teaching principles and the indicators of realistic mathematics education (section 3.2.1) continually played a part in preparing, recording and making MILE accessible.

Exemplary for the program of primary education. The digitized primary mathematics education that has been stored in MILE has been characterized as a representation of

‘real teaching practice’. However, because it is not possible to capture the full range of practice in tapes taken during limited periods in different grades, the representation of the subject matter in MILE has to be considered as exemplary for the primary school.

What is meant by ‘exemplary’ is illustrated in the next examples. MILE contains:

- Recordings of a learning strand for percentage in grades 5 and 6, with special attention to going through a learning strand, the procedure of problem-oriented education, the evaluation of certain subject matter, and differences between children.

- A theme (the restaurant) in grades K-1, with special attention on teaching young children, the development of number sense, learning in context, and interaction in classroom discussion.

- Mathematic activities in daily life, ‘the problem of the week’ in grades 2, 4 and 6.

- Practicing the multiplication tables and a clinical interview with two pupils of grade 2 who differ in insight and attitude about the tables.

- A pupil explaining a mathematical production.

- A pupil taking over the leadership of a group.

Through outlines. MILE offers two kinds of outlines. The first are concerned with learning strands such as multiplication tables or percentages. The second follow individuals’ learning of mathematics, especially in the recordings of grades 2, 4 and 6, where the same children are shown at intervals two years apart. One can observe the children during classroom interaction, individual activities, group work, and interviews.

Reflective practice. MILE includes recording of the professional talks between the two job-sharing teachers about the progress of mathematics education in their grade 2 class.

Much of the (tacit) practical knowledge of these teachers became explicit as they reflected on their practice before and after the lessons.

Theoretical charge. Without violating the authenticity of the digitized practice, the director emphasized certain situations during recording; hence sometimes there was exclusive attention to the teacher or to a pupil. For instance, the director could decide to tape one child for a longer time, to capture interesting elements such as the specific effect of a context or a clever or invalid use of a model by a pupil trying out a strategy.

Next, we describe what investigations of good practice, characterized in the previous section, brought to student teachers during their first expeditions in MILE.

3.5 The first exploratory researchⁱⁱ

3.5.1 Research question

To get insight into the (optimal) possibilities of MILE as good practice for teacher education, exploratory research was carried out using ten lessons on CD-roms and the first version of the search engine (Oonk, 1999). The study was focused on knowledge construction, but also with an attempt to provide insight into the investigation process experienced by two student teachers and the benefits of their related discourse and collaboration.

The research question was: What is the character of the investigation process of student teachers in MILE and what is the output of their learning process in terms of knowledge construction?

A total of 15 meetings, eight of which were two-hour sessions with the researcher, were audio recorded.

3.5.2 Learning by investigating the recorded teaching practice

Our approach resembled that used in the Student Learning Environment approach developed at Michigan rather than the more academic approach of Mousley and Sullivan (1996). But in contrast to the Student Learning Environment approach, student teachers could investigate the digitized practice of MILE by means of keywords derived from their own research questions. There was little steering: the student teachers could formulate, reformulate, and revise their own questions. The rationale for this approach was that investigating practice by focusing on one’s own pedagogical problems, especially in tandem with the coupled reflective activities, will contribute to self- regulated professional development (Zeichner & Noffke, 2001).

ii This section is based on: Oonk, W. (1999). Pioniers in MILE. Een exploratief onderzoek [Pioneers in MILE. An exploratory study]. MILE-reeks nr. 9. [MILE series nr. 9] Utrecht:

Freudenthal Instituut.

3.5.3 The process

In this section we describe an overview of the investigation process of two excellent student teachers of the primary teacher training college at Amsterdam (Hogeschool van Amsterdam) and their highly motivated coach/researcher.

The fifteen meetings developed through three stages, which naturally flowed from the process of the student teachers’ investigation. The first was orientating to MILE by getting acquainted with the teachers Minke and Willie of grade 2, the pupils, the subject matter, and the techniques for searching in the learning environment. The student teachers Dieneke and Hayet had at their disposal a computer, ten lessons of grade 2 on CD-rom, the ‘Telling stories of grade 2’ (Oonk, 1997), the pupils’ textbooks, and the teachers’ guide for the mathematics textbook series ‘De wereld in Getallen’ [The World in numbers]²⁵. The first meeting started with a short discussion about the goal and the schedule of the learning project and continued with an orientation to the technique and content of MILE. The following quotes from the student teachers give a representative idea of their reactions to the first meeting:

Beautiful, such a transfer you never can see in your school practice, that happens mostly by phone.

Children can suddenly have an ‘aha’ experience, as in an active moment after a passive period of language acquisition.

In this first period, student teachers got used to the styles and personalities of the MILE teachers. Their comments gradually shifted from impulsive perceptual reactions to reflective discussions. Often a remark led to (sometimes heavy) discussions, which frequently led to re-viewing of the video.

The second stage was learning to investigate. The publication ‘Telling stories of grade 2’

(Oonk, 1997) offered the student teachers a point of departure for searching and studying video fragments. However, this was not sufficient, and the students soon reverted to trial and error. This led Hayet to create a step-by-step plan for searching and observing the ideas and for formulating (new) questions.

The third stage was directed research. It began when the student teachers decided to make a video to orient imaginary peers to MILE. They thought that this would allow them to show their own learning, make available an ‘orienting adventure in MILE’ for young future teachers, and inject an element of originality to their report and presentation. By this time, Dieneke and Hayet had acquired experience in using MILE and investigating their own learning questions.

The culmination of the investigation consisted of an oral exam, a written report, and a presentation. Audio recordings during the discourse, e-mail communications, and written reflections document the collaboration and the individuals’ learning and thinking processes.

3.5.4 Incentives in the learning environment

We next discuss what the first, simple version of MILE offered the two student teachers and their coach/researcher, and focus on the question: What makes MILE educative?

We probe to answer that question by elaborating main incentives in the learning environment.

Search words, search questions, and learning and investigation questions.

In their investigations in MILE, the two student teachers were limited by the simple search engine and their own search questions. In the first stage they often used ‘Telling stories of grade 2’ (Oonk, 1997) as a source for finding search words (e.g., mental action, ‘playing Dumb August’²⁶, ‘egg box’²⁷). To some extent the ‘The World in numbers’ textbook and the teacher’s guide served the same function. To prepare for meetings, they used the textbook to plan the same lesson as the lesson taught by the MILE teacher, and then observed that lesson. This made the subsequent discussion more reflective than it had been previously. They raised questions such as: Did I devote sufficient time in my lesson to dividing numbers? Did I leave too much to the children?

Can they actually estimate prices?

After seeing how the video teacher approached the lesson, they would draw comparisons and perhaps revise their own lesson plans.

Revealing practical knowledge. The student teachers were impressed by what they saw in MILE. The discourse often ended in personal analyses from different points of view.

They called upon mathematics aspects but also took pedagogical and content pedagogical positions. From the beginning they were convinced that they could learn a lot from MILE teachers. Dieneke explained: “What are the ‘good questions’ that Minke asks? I noted how well she formulated an exercise: ‘If you have thought and drawn one way, try to think of another one.’ I would not mind hearing this remark a thousand times so I can imprint it in my mind. Instead of a compulsory exercise such as ‘Give at least 3 solutions,’ Minke shows she appreciates one solution and she encourages the pupils to think further. In my opinion, her choice of words is a clear example of good teaching.”

However, Dieneke did not accept Minke’s practical knowledge unquestioningly. She analyzed, interpreted, and put forward arguments to substantiate what she believed she had observed. In doing so, she touched on the practical knowledge that appeared to guide Minke’s actions (in effect, unpacking this practical knowledge). In addition, she recognized

‘usable material’ even in the routines of the daily classroom activities. For example, Dieneke learned that Willie – Minke’s peer teacher – could quickly quiet the children and get their attention by remarking: “Everyone turn the calculator in your head on.”

From the beginning Hayet philosophised about the additional value of MILE as compared with teaching practice or lectures, and she also recognized the practical

knowledge of the expert teachers in MILE. She was especially impressed by the interviews, in which the teachers told about their plans for the next lesson: “Of the three types of video (transfer, interview, lesson), the interview made the most impression on me. It was like looking into the head of the teacher and finding out secret information.

Going through a lesson step-by-step in this way is very practical and concrete. None of my tutors ever did this for me.”

Theory from practice. Searching for a direction to their investigation, Dieneke and Hayet got the idea to design a video for their peer first year student teachers, inspired by a lesson in which teacher Willie introduced the five times table. They became interested in the ways that Willie translated concrete material to the children, the children worked with that material, and the material precipitated mental action. By connecting to relevant theory, Dieneke and Hayet would make a statement about encouraging the rise from material to mental level in children’s learning. They formulated questions, made notes, then started theorizing: “We have made the following statement based on this video: ‘If the transition from concrete to mental action does not take place in sufficiently small and logical steps, the (material and mental) actions will remain separated from each other. The main objective is to couple these actions together (…).’ ”

Theory of practice. After the above mentioned discussion, the teacher educator wrote an extensive (electronic) annotation to make the student teachers aware of the distinction between a mechanistic ‘step-by-step’ approach and realistic didactics in which properly conceived ‘learning’ jumps in teaching are encouraged. He also focused on theoretical views on different levels of subject matter and learning processes applied to the structure of mathematics courses. The student teachers became very interested as they addressed these problems. Dieneke recognized the danger of misunderstanding rules from her own past education. In the next meeting, she revised a previous statement about a video fragment in which a pupil shows that thinking of egg boxes helps her interpret 43 as 40 (four egg boxes) + 3 (separate eggs): “This statement applies to small logical steps, raising pupils’ levels, and direct support. Support and raising pupils’ levels are similar concepts.

The material is first used as a support. When pupils no longer need it and begin to construct mentally, their level of competence rises. Materials always help and support, provided you introduce them properly. If you do not do this, they are only extra ballast and lead to confusion. The fragment ‘Think of egg boxes’ is a good example of this since Minke had not referred to them before and ‘suddenly’ introduced them without moving through a sequence of small logical step towards them (…).”

The practical meaning of theory. The discussion about how to raise levels of thinking required student teachers to find relevant theoretical knowledge. They questioned the teacher educator and studied relevant articles and textbooks. They realized that MILE

contains information (practical knowledge) that cannot be found in textbooks or teachers’

guides and compared the theory taught in lessons at college with the observed theory linked to the real-life situations in MILE. For example, by relating theory to practice, Hayet became aware that the terms concrete, abstract, mental, and formal initially put her on the wrong track: “In my opinion, ‘the abstract level’ means formal mathematics.

‘Mental actions with material’ contains the word mental, but does not belong on that abstract level. It should be placed on the concrete/material level. Actions with material are performed ‘in your head’ (it is not a physical action), but they are concrete, or in other words, conceivable and meaningful (…).”

The discourse as driving the learning process. The discourse about the practice in MILE was elaborated in corridor chats and e-mail communications. The student teachers were aware of the influence of the discourse on their cooperation and their learning processes. As Hayet put it: “I find it rather comical. If I had watched the video on my own, I would probably have missed the whole scene. The discussion that was brought about by that ‘small interesting incident’ is for me just like the didactics involved the most instructive part of the whole meeting. Another good thing about the discussions is that we start with critically thinking about what Minke does and why she does it. Is it part of her conscious strategy? And then the emphasis shifts to our own experiences and didactic considerations.”

One’s own practice as reflective. The practice in MILE engendered student teachers’

linkages to their own teaching practice. This happened in a natural way as they analyzed and compared the actions of the MILE teacher to their own experiences or anticipated future practice. Hayet compared her failed experience with ‘Playing Dumb August’ of her pupil Keltoum to the successful experience of MILE teacher Minke. Placing the

‘Dumb August’ approach in a wider perspective, she started formulating questions and hypotheses. She wondered about the relationship between one’s approach to ‘Dumb August’ and learners’ attitudes about making mistakes: “When you want to teach children to investigate mathematics (i.e., try out more than one strategy), it is important that you see making mistakes as part of the process. If you do not, you go straight back to mechanistic viewpoints: there is one way to solve a problem – the right way, mistakes are bad, and children who make mistakes are stupid. This MILE episode made me realize the strength, but also the possible dangers of the ‘Dumb August’ method.”

Final presentation. Both student teachers tell a lot of stories about their pioneering in MILE (Blikslager & De Bont, 1997; Oonk, 1999). In the closing presentation of their assignment, Hayet explained how her investigation in MILE had made her aware of what is behind theory in the lectures she hears in teacher education courses. She believes that MILE stories will help her keep in mind the connection between theory and practice.

3.5.5 The main findings of pioneering

The pioneers’ experiences during their investigations of the first version of MILE can be interpreted from four points of view.

The investigating process. In the course of the exploratory research, the investigating process was portrayed as the vehicle of the student teachers’ learning process. In other words, carrying out investigations kept the learning process in motion. The investigating process in MILE is a cyclical process of planning, searching, observing, reflecting, and evaluating. Its relationship to action research (Carr & Kemmis, 1986; Jaworski, 1998) is obvious, although there are differences in reasons, goals, and content.

The discourse. The discourse that was put together during the meetings can be seen as the driving force behind the learning process. The discourse can provide opportunities for the emergence of new insights, incentives for searching further, and impetus for choosing a theoretical line of approach or developing one’s own theorizing. The discussions observed during the investigations of Dieneke and Hayet have the characteristics of ‘reflective discourse’ (Cobb, McClain, & Whitenack, 1997), which we treat as a socio-constructive adaptation of Schön’s reflective conversation (Schön, 1983).

Levels of knowledge construction. The analysis of Dieneke and Hayet’s investigation process has provided insight into knowledge construction at four levels. These levels are observable particularly in the discussions and the reflective notes.

Firstly, knowledge can be ‘taken over’ from the teachers in MILE; student teachers expand their own didactic repertoires through assimilation of the practice knowledge contained in MILE. Assimilation occurs if the student teacher indicates that he or she would like to implement the knowledge of the MILE teacher (as observed, without adaptation to his or her own purposes).

Secondly, adaptation and accommodation of practice knowledge is a second level of knowledge construction. Users of MILE can modify the repertoires of the MILE teacher to suit their own purposes; they expand their own repertoires by modifying the MILE teacher’s repertoire. Knowledge construction at this second level can have a greater impact on the student, especially if the student has to adjust his or her personal beliefs.

In this case, something changes in the cognitive or affective structure that we call practice knowledge. For this reason, this is called accommodation. It also has some of the characteristics of what Perry calls relativism. Knowledge on the first level that is constructed on the authority of the ‘model teacher’ has more of the characteristics of Perry’s ‘dualism’ (Hofer & Pintrich, 1997).

Thirdly, the student teachers display an even higher level of knowledge construction when they establish (new) links between the events in MILE and events from their own trainee practice and related theory. This is the level of ‘integrating theory,’ in which

they might (re)consider didactic insights and points of view. They ask themselves questions about the situation observed in MILE and make links with what they find in the literature. The teacher educator has a task in this respect, namely to respond effectively to the questions posed by the student teachers. Using theoretical reflections – as annotations – about given real practice situations that intertwine the investigation of practice with the examination and development of theory, the teacher educator puts students on the track of explanatory theory. The theory is understood and remembered in the context of a scene in MILE, usually in the form of a story of the events that occurred in MILE.

The fourth and highest level of knowledge construction – the level of theorizing – manifests itself when the investigators in MILE design their own local theories. They build up ideas about causes and consequences through the observation and interpretation of fragments they find themselves. The ensuing discourse can have a specific theoretical orientation and provide motivation for follow-up investigations.

3.6 Larger scale field tests

Since the seventies, Dutch primary teacher training colleges have created a strong infrastructure for mathematics education, in which teacher educators and curriculum designers collaborate in a Mathematics and Didactics program for future teachers. The teacher educators meet annually at conferences. This infrastructure was used to introduce MILE and invite math teacher educators to use and assess it. From the beginning more then twenty educators were participating in the workshops, discussing the state of the art of MILE, and anticipating its future use in their own colleges.

Shortly after the first exploratory research at the primary teacher training college in Amsterdam (section 3.5), five pilot studies were started at fourteen other Colleges (Goffree, 1998). In these pilots, three aspects of MILE were field tested: using MILE within the local curriculum, the optimal use of MILE by student teachers, and the relationship between teaching practice in schools (fieldwork) and MILE. All pilots addressed the issue of MILE’s position between theory and practice in teacher education. In the meantime the basic MILE program had been increased to 30 gigabytes consisting of 23 lessons of grade 2 and five lessons of grade 5 (percentages) at a different elementary school. Student teachers could use the search engine and the archive now, without having to change disks.

Although approaches to MILE varied at the different locations (size of groups, the scale of the research, the amount of face-to-face instruction, collaboration, coaching, assignments, and reports), the common output provided a lot of reflection on the creation of a learning environment for future teachers. Studying the output, an obvious question arose: What should be added to MILE in order to help student teachers to

enlarge and deepen their practical knowledge? Assignments and reports provided vehicles for addressing this question.

The outcome of the analysis yielded answers to main questions according to the desired improvement of MILE.

What practical knowledge do student teachers have available at the start of their investigation? Like the pioneers (Dieneke and Hayet), the participants of the pilot projects were (mainly) last year students. Their practical knowledge became apparent during observations of lessons when they were asked to question MILE. For instance:

Would the teacher indeed be able to teach this subject matter interactively?

How does the teacher deal with low achievers?

Does the teacher focus students’ attention on different strategies?

These student teachers apparently know a lot about math teaching; now they want to see concrete examples in practice. Sometimes their practical knowledge seemed to hold theoretical elements.

How was MILE experienced as a learning environment?

Their subsequent statements indicated that the student teachers in the pilots experienced MILE as:

- A reservoir of instructive events.

- Storage of all sorts of aids to use in math classes.

- A place to work for teachers and pupils.

- Practice in which ‘the theory’ becomes apparent.

- A set of opportunities to show one’s professionalism.

- ‘Something else’ rather than teaching practice.

Which self formulated learning questions initiated student teachers’ investigations?

In most pilots, the teacher educators presented good reasons to start an investigation. A successful reason was created by having student teachers prepare a lesson that would be observed subsequently in MILE. Other reasons were found in fieldwork, in lectures, in the storybook (Oonk, 1997), or in the theory. An example of such a learning question, which subsequently led to investigation questions and searching words, was “What is the nature of collaboration between a gifted student and the other students in a small cooperative group?” Other learning questions addressed using the blackboard, the teacher’s behavior, the learning process of one selected pupil, classroom interaction, group work, mental arithmetic, and estimation.

What did the video-pictures of MILE evoke in student teachers?

MILE sought to represent practice, so it is interesting to know which aspects of practice student teachers attend to in MILE. The reports mention a number of favorite fragments,

both from student teachers during their first exploration and from teacher educators who wanted to illustrate practice using MILE.

What did the student teachers say they had learned from MILE?

The student teachers’ statements about what they had learned from their investigations in MILE were fairly vague. Second-year student teachers believed that learning from the MILE teacher is the same as imitating the MILE teacher. Older year student teachers pointed to the transfer talks between the job-sharing MILE teachers and to the number line used as a model during instruction. More profound was the reaction of a fourth-year student teacher who wrote: “I learned that during a math lesson more happens than you could imagine in advance—much more than the teacher can see. Because of MILE you become aware how children think, more so than you do from just reading theory books.”

The learning attributed to MILE varied with the context in which the question was asked, the nature of the studied fragments, and the student teachers’ reflective abilities. Just as in the exploratory research on the pioneers, the pilot projects suggest that methods for learning about practice need to be learned along with practice itself. Both projects underscore the value of discourse for the learning process. Furthermore, having some basic practical knowledge at one’s disposal, taking initiative, posing one’s own learning questions, considering one’s own past in math education, and moving beyond an initial critical attitude towards the MILE teacher benefits learning by investigating MILE.

In order to transfer MILE into ‘good practice for future teachers,’ it appeared to be necessary to supply MILE with ‘reasons’ to start investigations, to help student teachers to engage in the desired activities and reflections. Actually from this moment the need for structuring the learning environment became more and more manifest.

3.7 Making MILE educative

In section 3.5.4 we discussed the question: ‘what makes MILE educative?’ by elaborating the main incentives in the learning environment. The analyses of the research results as described in section 3.5.5 and 3.6, led to refining of the answers to that question. We defined therefore ‘educative’ as enabling future teachers to acquire practical knowledge, and investigated the conditions, circumstances, and means needed to accomplish that goal. The following inventory shows the main part of the observerved conditions and means.

Initial achievement level of the student teachers:

- It appeared that student teachers learned something more than imitating in MILE if they already had a basic practical knowledge; obviously, student teachers cannot start investigations without at least some reflected experience in classrooms.

- Searching in MILE has to take place in an investigation context, preferably on the basis of searching words that arise out of a learning question.

- Various reasons to start an investigation can be constructed by tutor or tutee in order to formulate learning questions.

- Formulating personal learning questions needs directed support by a coach who is familiar with the contents of MILE.

- Student teachers who want to start an investigation in MILE should first have practiced learning by investigating and observing and interpreting MILE fragments.

- New student teachers begin with a personal belief about good practice.

Acquiring practical knowledge as narrative knowing:

- The meaning of practical knowledge can be clarified by discussing and analyzing the transfer talks between the two MILE teachers at grade 2.

- The preliminary talks (interviews) with the teachers, when they put into words what they intend to do during the next lesson, provide attention points for observing.

- The book ‘Telling stories of grade 2’ (Oonk, 1997) can be utilized as a source book for investigating MILE.

- The investigating process is the vehicle for the student teachers’ learning.

- The discourse about the practice drives student teachers’ investigating process.

- Meaningful assignments are needed to support student teachers’ progress with MILE.

- Teaching stories about the events in MILE can be best written by the student teachers as case studies.

- Studying pedagogical and didactical actions of the teacher in MILE motivates student teachers to compare MILE with their own fieldwork.

- Surprising moments of pupils’ learning might help student teachers to connect with their own primary school experiences.

- To stimulate narrative knowing, student teachers may collect favorite narratives linked to MILE videos.

- Input from the MILE tutor usually deepens student teachers’ learning.

- Student teachers have to learn to participate in reflective discourse.

- Collaborating generally stimulates the continuity and profundity of an investigation.

- Developing ‘didactical productions’ creates an appropriate context for investigating in a narrative, constructive, and reflective way.

- Preparing a MILE lesson before observing it helps students to make sense of the discourse.

- Student teachers report valuable experiences when theoretical concepts or reasoning are actualized through observation of practice, as when the MILE teacher organizes a classroom discussion about pupils’ mistakes or when the student teachers recognize differences between children.

Limitations and bottlenecks.

In this period the MILE team tried to adapt the idea of a Knowledge Forum (Bereiter &

Scadamalia, 1997) in order to improve the discourse of the student teachers, using its functions such as special interest groups and e-mail. The Knowledge Forum provides a structure for knowledge construction by remote cooperating students. However, this attempt had to be dropped because of technical problems and the problem of the narrative organization of practical knowledge.

The research revealed some important bottlenecks in the way to enable future teachers to acquire practical knowledge:

- Although the MILE team supported the open approach of the student teachers’

environment, the field tests pointed towards the need for more structuring and scaffolding of the student teachers’ learning by investigating.

- Student teachers usually require support in learning to relate theoretical knowledge to the practice in MILE.

- Student teachers do not realize immediately that theoretical knowledge is a valuable addition to practical knowledge.

Research and development of the educative component of MILE had to be continued, because the program did not yet enable student teachers to carry on reflective conversations with practice (as mentioned by Schön, 1983) or relate known theory to observed practice. The dangers of superficial reflection on practice are pointed out by Verloop: “It is worthwhile to reflect on one’s teaching, but at some stage questions should be asked about the quality of that reflection. For example, to what extent does the reflection take relevant external knowledge into account, what exactly does reflection improve in the actual teaching process, and to what extent is the reflection open to external scrutiny and critique?” (Verloop, 2001, p. 436).

The next section will describe the research that goes into the question of whether student teachers indeed use theory when studying practice.